Synthesis,characterization, molecular docking studies and in vitro screening of new metal complexes with Schiff base as antimicrobial and antiproliferative agents

A series of Cu(II), Co(II), Pd(II), Pt(II), Zn(II), Cd(II) and Fe(III) complexes were designed and synthesized using Schiff base 1‐phenyl‐2,3‐dimethyl‐4‐(N‐3‐formyl‐6‐methylchromone)‐3‐pyrazolin‐5‐one (HL). The new metal complexes were investigated using various physicochemical techniques including elemental and thermal analyses, molar electric conductivity and magnetic susceptibility measurements, as well as spectroscopic methods. Also, the crystal structures of ligand HL and the Pd(II) complex were determined using single‐crystal X‐ray diffraction analysis. For all compounds, the antimicrobial activity was studied against a series of standard strains: Staphylococcus aureus, Bacillus cereus, Enterococcus faecalis, Escherichia coli, Acinetobacter baumannii, Candida albicans, Candida krusei and Cryptococcus neoformans. The in vitro antiproliferative activity of the ligand and complexes was evaluated against ten cancer cell lines: MSC, A375, B16 4A5, HT‐29, MCF‐7, HEp‐2, BxPC‐3, RD, MDCK and L20B. At 10 μM concentration a significant cytotoxic effect of the Co(II), Pd(II) and Cd(II) complexes was observed against B16 4A5 murine melanoma cells. The Zn(II) complex is active against HEp‐2, RD and MDCK cancer cell lines, where IC₅₀ values vary between 1.0 and 77.6 and for BxPC‐3 the activity index versus doxorubicin is 3.7 times higher.     

On the Beurling dimension of exponential frames

We study Fourier frames of exponentials on fractal measures associated with a class of affine iterated function systems. We prove that, under a mild technical condition, the Beurling dimension of a Fourier frame coincides with the Hausdorff dimension of the fractal.     

Generalized Walsh Bases and Applications

We investigate convergence properties of generalized Walsh series associated with signals f∈L ¹[0,1]. We also show how the dependence of the generalized Walsh bases on N×N unitary matrices allows for applications in signal encoding and encryption, provided the signals are piece-wise constant on N-adic subintervals of [0,1].     

On the characterization of the compact embedding of Sobolev spaces

For every positive regular Borel measure, possibly infinite valued, vanishing on all sets of p-capacity zero, we characterize the compactness of the embedding ${W^{1,p}({\mathbb R}^N)\cap L^p ({\mathbb R}^N,\mu)\hookrightarrow L^q({\mathbb R}^N)}$ in terms of the qualitative behavior of some characteristic PDE. This question is related to the well posedness of a class of geometric inequalities involving the torsional rigidity and the spectrum of the Dirichlet Laplacian introduced by Pólya and Szeg? (Isoperimetric inequalities in mathematical physics, Annals of mathematics studies, 1951). In particular, we prove that finite torsional rigidity of an arbitrary domain (possibly with infinite measure), implies the compactness of the resolvent of the Laplacian.     

On Smooth Maps with Finitely Many Critical Points: Addendum

The paper is an addendum to D. Andrica and L. Funar, ‘Onsmooth maps with finitely many critical points’, J. LondonMath. Soc. (2) 69 (2004) 783–800.     

Measurement of natural radioactivity and radiation hazards for some natural and artificial building materials available in Romania

As building materials are known to be the second source regarding high radon concentrations, it is very important to determine the amounts of natural radionuclides from every building material in use. In the present study the most frequently used Romanian natural (sand, gypsum, limestone) and artificial (portland cement, lime, clinker, electrofilter powder, fly ash, cement-lime plaster mortar, cement plaster mortar) building materials were analyzed. The absorbed dose rate and the annual effective dose equivalent rate for people living in dwelling buildings made of these building materials under investigation were also calculated. The analysis was performed with gamma-ray spectrometry, with two hyper-pure germanium detectors. The activity concentrations of natural radionuclides were in the ranges: 5.2–511.8 Bq kg^?1 for ²²⁶Ra; 0.6–92.6 Bq kg^?1 for ²³²Th and <1–1,720.7 Bq kg^?1 for ⁴⁰K, respectively. The radium equivalent activity in the fifty-one (51) samples varied from 9 to 603 Bq kg^?1. By calculating all the radioactivity indices (Ra_eq, H _ext, I _α, I _yr) it was found that all the building materials under investigation can be used to erect dwelling buildings. Except for sample SA6, SA7 and SA11 among the natural building materials and sample SG1, SG2, FAH1, CLM1, CM1 among the artificial building materials that are considered hazardous materials when are used in large quantities.     

Characterization of the shape stability for nonlinear elliptic problems

We characterize all geometric perturbations of an open set, for which the solution of a nonlinear elliptic PDE of p-Laplacian type with Dirichlet boundary condition is stable in the L^∞-norm. The necessary and sufficient conditions are jointly expressed by a geometric property associated to the γp-convergence.If the dimension N of the space satisfies N−1<p?N and if the number of the connected components of the complements of the moving domains are uniformly bounded, a simple characterization of the uniform convergence can be derived in a purely geometric frame, in terms of the Hausdorff complementary convergence. Several examples are presented.     

Do Optimal Shapes Exist?

This paper surveys the talk given by the author at the “Seminario Matematico e Fisico di Milano” in November 2006. It deals with the existence question for shape optimization problems associated to the Dirichlet Laplacian. Existence of solutions is seen from both geometrical and functional (γ-convergence) point of view and is discussed in relationship with the optimality conditions and numerical algorithms. Several examples are given concerning isoperimetric inequalities for eigenvalues and shape control problems. Received: August 2007     

Bimodal, dimetallic lanthanide complexes that bind to DNA: the nature of binding and its influence on water relaxivity

UV-visible titrations, (1)H NMRD experiments and molecular docking studies show that emissive anthraquinone appended dimetallic lanthanide complexes bind to DNA. The strength of binding and the observed relaxivity behaviour depend on the nature of the substituted anthraquinone core.     

Hilbert Series and Lefschetz Properties of Dimension One Almost Complete Intersections

We generalize some results about the graded Milnor algebras of projective hypersurfaces with isolated singularities to the more general case of an almost complete intersection ideal J of dimension one. When the saturation I of J is a complete intersection, we get formulas for some invariants. Examples of hypersurfaces V: f = 0 in ?ⁿ whose Jacobian ideals J satisfy this property and with nontrivial Alexander polynomials are given in any dimension. A Lefschetz property for the graded quotient I/J is proved for n = 2 and a counterexample due to A. Conca is given for such a property when n = 3.